Pics & History of your Empire

[NodachiSam]

The higher your kings influence the better your princes will be when they turn 15. Getting high or lower influence before or after they turn 15 doesn't affect them. Only the influence at the time. However, if your kings influence gets too high your princes can "roll over" and become really crappy. So if your kings influnce is at 7 or 8 you princes might have likewise attributes but at 9 or 10 there is a chance you'll get low values princes. It sort of encourages pacing yourself in a way. I think there is also a random element involved.